ivj.wJL.Lw.Ln Substituting this value of G in the torque equation we have T doo 0 _,.. 0 I-rr = - 2FDCOS- dt 2 h FIRST APPROXIMATION. When 0 and <£ are small the following relations give close enough approximations. m 1 0 T = img, cos- = 1, 2 D JDO ==: 6</>j sin <j!> == 0== ~r 0. Making these substitutions in the torque equation we get du _ __ m^D2 which is the equation of simple harmonic motion. Therefore mg is the period of the motion. SECOND APPROXIMATION. From Fig. 143 we have FIG. 143. and ea'= Zsin</>= 2Dsin- - -2 Therefore and 2D . 0 sin 0 = sin ~ I 2i T = sin2 ^ * The line ea' is considered as an arc of each of two circles with centers at g and c.